Dissertation - HQ

102 Vertical distribution during ontogeny
Situate ontogeny
among other factors
Regression between
size and depth
Before exploring the differences between the distribution of ontogenetic
stages, one must make sure that other sources of variability are
not obscuring the potential effect of ontogeny. For example, post-flexion
larvae may be always a few meters lower in the water column than
pre-flexion larvae, but if both pre- and post-flexion larvae are within
0-20 m when the thermocline is at 30 m and within 20-50 m when it
is at 60 m, testing for a global difference in location through a rank
test such as the Wilcoxon-Mann-Whitney test will show nothing. One
solution is to work with the difference in z cm at each station, rather than
with the z cm themselves. Another possibility, which gives additional
information on the system, is to identify the other sources of variability
and eliminate them before testing the effect of ontogeny.
Successive regression trees were constructed to hierarchise the factors
influencing the distribution of z cms, and situate ontogeny among
those. The explanatory variables considered in addition to ontogeny
were taxonomic (family), temporal (time of day), geographic (latitude,
longitude, location with respect to the atoll, i.e. windward, leeward),
and hydrographic (depth of thermo-, halo-, pycnoclines, and of the
fluorometry maximum, mean current speed in the surface layer). When
several factors were correlated (e.g. depth of thermo- and pycnocline)
they were tested independently and only the most explanatory was
kept in the final tree. For discrete explanatory variables, the effect of
influential factors was investigated by comparing z cms between groups
(by taxon, by ontogenetic stage, etc.) using non-parametric tests for
differences in medians (Wilcoxon-Mann-Whitney and Kruskal-Wallis).
Homogeneity in variances was tested using the Fligner-Killeen test.
When variances were different between groups, the choice was made
to still use the same tests but to lower the significance level to 0.01, to
account for the higher risk of α-error (distributions were clearly nonsymmetric,
preventing the use of robust rank procedures, as mentioned
in the section “The problem of unequal variances”, page 99). The effect
of continuous explanatory variables was estimated by regression using
Generalised Linear Models with a gamma distribution of errors.
Over 3000 larvae were measured and their size was used as a proxy
for development. Indeed larvae usually reach a particular ontogenetic
level at a given size rather than at a given age 64 . They allowed to test
whether there was a continuous change in vertical distribution during
ontogeny (i.e. along with increasing sizes) through a regression analysis.
Of course size varies greatly among different fish taxa. Therefore, sizes
were normalised per taxon, i.e. for each of the lowest taxonomic units
identified, the size of the smallest fish captured was set to zero while the
size of the largest fish was scaled to one. While the ranges of ontogenetic
stages captured probably differed between taxa (i.e. size = 1 did not
correspond to the same point in development for all taxa), this brought
sizes on a more homogenous scale. Relative size and depth of capture
could then be compared. However, because of the patchiness in the
distribution of larvae, two larvae of the same taxon captured at the